Correspondence between two antimatroid algorithmic characterizations

The basic distinction between already known algorithmic characterizations of matroids and antimatroids is in the fact that for antimatroids the ordering of elements is of great importance. While antimatroids can also be characterized as set systems, the question whether there is an algorithmic description of antimatroids in terms of sets and set functions was open for some period of time. This article provides a selective look at classical material on algorithmic characterization of antimatroids, i.e., the ordered version, and a new unordered version. Moreover we empathize formally the correspondence between these two versions.